Deterministic relation between thermal-phonon dressings and Non-Hermitian multi-Fano interferences in ion-doped microcrystals

We report the multi-Fano interference obtained through the simultaneous acquisition of bright and dark states in different phase transitions of Eu3+: BiPO4 (7:1, 6:1, 1:1, and 0.5:1) and Eu3+: NaYF4 (1:1/4) crystals. We employ multi-dressed spontaneous four-wave mixing and multi-dressed fluorescence (multi-order) to optimize the strong photon-phonon nested dressing effect resulting in more obvious multi-Fano interference. Firstly, the multi-Fano is produced through interference in continuous and multi-bound states. Secondly, five multi-Fano dips originate from nested five dressings (one photon and four phonons) under symmetrical splitting of 7F1 energy level. We depict that the pure H-phase (0.5:1) sample exhibits the strongest photon-phonon dressed effect (five Fano dips). Further, we investigate high-order non-Hermitian exceptional points in multi-Fano interference by adjusting the ratio of Rabi-frequency to de-phase rate through nested photon and phonon dressing. Our experimental results are validated by theoretical simulations, which may be applied to designing optoelectronic devices such as multi-channel routers.